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A115788
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a(n) = floor(n*Pi) mod 2.
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6
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1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1
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OFFSET
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1
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COMMENTS
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The arithmetic mean (1/(n+1))*Sum_{k=0...n} a(k) converges to 1/2. What is effectively the same: the Cesaro limit (C1) of a(n) is 1/2. When we pick a term of the sequence at random, the probability of getting a '1' is 1/2. If we select a '1' randomly, the probability p11 of finding a '1' as the next term right of it is p11 = Pi - 3. If we select a '1' randomly, the probability p10 of finding a '0' as the next term right of it is p10 = 4 - Pi. Analogous statements hold for '0' --> '0' (p00 = p11) and '0' --> '1' (p01 = p10).
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LINKS
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FORMULA
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a(n) = floor(n*Pi) mod 2.
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EXAMPLE
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a(2) = 0 because floor(2*Pi) = floor(6.28... ) = 6,
a(8) = 1 because floor(8*Pi) = floor(25.13...) = 25.
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MAPLE
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a:= proc(n) Digits:= length(n) +15; floor(n*Pi) mod 2 end:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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